Welcome to the integers worksheets page at Math-Drills.com where you may have a negative experience, but in the world of integers, that's a good thing! This page includes Integers worksheets for comparing and ordering integers, adding, subtracting, multiplying and dividing integers and order of operations with integers.
If you've ever spent time in Canada in January, you've most likely experienced a negative integer first hand. Banks like you to keep negative balances in your accounts, so they can charge you loads of interest. Deep sea divers spend all sorts of time in negative integer territory. There are many reasons why a knowledge of integers is helpful even if you are not going to pursue an accounting or deep sea diving career. One hugely important reason is that there are many high school mathematics topics that will rely on a strong knowledge of integers and the rules associated with them.
We've included a few hundred integers worksheets on this page to help support your students in their pursuit of knowledge. You may also want to get one of those giant integer number lines to post if you are a teacher, or print off a few of our integer number lines. You can also project them on your whiteboard or make an overhead transparency. For homeschoolers or those with only one or a few students, the paper versions should do. The other thing that we highly recommend are integer chips a.k.a. two-color counters. Read more about them below.
General Use Printables
Comparing & Ordering Integers Worksheets
For students who are just starting with integers, it is very helpful if they can use an integer number line to compare integers and to see how the placement of integers works. They should quickly realize that negative numbers are counter-intuitive because they are probably quite used to larger absolute values meaning larger numbers. The reverse is the case, of course, with negative numbers. Students should be able to recognize easily that a positive number is always greater than a negative number and that between two negative integers, the one with the lesser absolute value is actually the greater number. Have students practice with these integers worksheets and follow up with the close proximity comparing integers worksheets.
By close proximity, we mean that the integers being compared differ very little in value. Depending on the range, we have allowed various differences between the two integers being compared. In the first set where the range is -9 to 9, the difference between the two numbers is always 1. With the largest range, a difference of up to 5 is allowed. These worksheets will help students further hone their ability to visualize and conceptualize the idea of negative numbers and will serve as a foundation for all the other worksheets on this page.
Adding & Subtracting Integers Worksheets
Have you heard about two-color counters and how they can make your life much easier while helping students understand integers better? Sure, you could just teach them the the ++, +-, -+, and -- rules, but then they would have no color in their lives. Two-color counters are usually plastic chips that usually come with yellow on one side and red on the other side. They do come in other colors, so you'll have to use your own colors in our description.
Adding with two-color counters is actually quite easy. You model the first number with a pile of chips flipped to the correct side and you also model the second number with a pile of chips flipped to the correct side, then you mash them all together, take out the zeros (if any) and voila! you have your answer. Since there are a few confused faces in the audience, let us explain a little further.
When we say, the correct side, we mean use red for negative numbers and yellow for positive numbers. You would model -5 with five red chips and 7 with seven yellow chips. Mashing them together should be straight forward. Since you are adding, you put the two groups of chips together, being careful not to flip any of them in the process, of course. Taking out the zeros means removing as many pairs of yellow and red chips as you can. You do this because -1 and 1 when added together equals zero (this is called the zero principle of all things). If you remove the zeros, you don't change the answer at all. The benefit of removing the zeros, however, is that you always end up with only one color and by consequence, the answer to the integer question.
Subtracting with integer chips is a little different. Integer subtraction can be thought of as removing. To subtract with integer chips, begin by modeling the first number (the minuend) with integer chips. Next, remove the chips that would represent the second number from your pile and you will have your answer. Unfortunately, that isn't all there is to it. This works beautifully if you have enough of the right color chip to remove, but often times you don't. For example, 5 - (-5), would require five yellow chips to start and would also require the removal of five red chips, but there aren't any red chips! Thank goodness, we have the zero principle. Adding or subtracting zero (a red chip and a yellow chip) has no effect on the original number, so we could add as many zeros as we wanted to the pile, and the number would still be the same. All that is needed then is to add as many zeros (pairs of red and yellow chips) as needed until there are enough of the correct color chip to remove. In our example 5 - (-5), you would add 5 zeros, so that you could remove five red chips. You would then be left with 10 yellow chips (or +10) which is the answer to the question.
Multiplying & Dividing Integers Workshets
Multiplying integers is normally where students learn the general rules for multiplying negatives and positives. Summarized, they are ++ = +; -- = +; +- = -; and -+ = -. In other words, multiplying two positives or two negatives together results in a positive products, and multiplying a negative and a positive together results in a negative product.
In order to develop a deeper understanding of these rules, it is nice to think of an example from outside of school such as a bank and its loan clients. For simplicity sake, we'll use low numbers, but the actual numbers will be greater (maybe think in terms of thousands of dollars). Let's say the bank gets 3 new loan clients and each customer borrows $5. From the bank's perspective, they have gained three customers (+3) and lost $5 from each one (-5). In total, they have lost 3 x (-5) = -$15. From the clients' perspective, they each gained $5, so they would all be in positive territory 3 x 5 = $15. If the clients all paid back their loans, the bank would lose the 3 customers